Related questions

Sum matrix elements group by indices in Python

2018-07-10 14:54 Mortafix imported from Stackoverflow

I have two matrix (same row and column): one with float values, which are grouped by indices in the other matrix. As a result, I want a dictionary or a list with the sums of the elements for each index. Indices always start at 0.

A = np.array([[0.52,0.25,-0.45,0.13],[-0.14,-0.41,0.31,-0.41]])
B = np.array([[1,3,1,2],[3,0,2,2]])

RESULT = {0: -0.41, 1: 0.07, 2: 0.03, 3: 0.11}

I found this solution, but I'm searching for a faster one. I'm working with matrix with 784 x 300 cells and this algorithm takes ~28ms to complete.

import numpy as np

def matrix_sum_by_indices(indices,matrix):
    a = np.hstack(indices)
    b = np.hstack(matrix)
    sidx = a.argsort()
    split_idx = np.flatnonzero(np.diff(a[sidx])>0)+1
    out = np.split(b[sidx], split_idx)
    return [sum(x) for x in out]

If you can help me find a better and plain solution to this problem, I'll be grateful!

EDIT: I made a mistake, time to complete is ~8ms in a 300*10 matrix, but ~28ms in a 784x300.

EDIT2: My A elements are float64, so bincount give me ValueError.

3 answers

  • answered 2018-07-10 15:16 Eelco Hoogendoorn

    The numpy_indexed package has efficient and simple solutions to this problem (disclaimer: I am its author):

    import numpy_indexed as npi
keys, values = npi.group_by(B.flatten()).sum(A.flatten())

  • answered 2018-07-10 15:16 user3483203

    You can make use of bincount here:

    a = np.array([[0.52,0.25,-0.45,0.13],[-0.14,-0.41,0.31,-0.41]])
b = np.array([[1,3,1,2],[3,0,2,2]])

N = b.max() + 1
id = b + (N*np.arange(b.shape[0]))[:, None] # since you can't apply bincount to a 2D array
np.sum(np.bincount(id.ravel(), a.ravel()).reshape(a.shape[0], -1), axis=0)

    Output:

    array([-0.41,  0.07,  0.03,  0.11])

    As a function:

    def using_bincount(indices, matrx):
    N = indices.max() + 1
    id = indices + (N*np.arange(indices.shape[0]))[:, None] # since you can't apply bincount to a 2D array
    return np.sum(np.bincount(id.ravel(), matrx.ravel()).reshape(matrx.shape[0], -1), axis=0)

    Timings on this sample:

    In [5]: %timeit using_bincount(b, a)
31.1 µs ± 1.74 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

In [6]: %timeit matrix_sum_by_indices(b, a)
61.3 µs ± 2.62 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

In [88]: %timeit scipy.ndimage.sum(a, b, index=[0,1,2,3])
54 µs ± 218 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

    (scipy.ndimage.sum should be faster on much larger samples)

  • answered 2018-07-10 15:40 Thomas Baruchel

    The following solution, relying on scipy.ndimage.sum is highly optimized for speed:

    import numpy as np
A = np.array([[0.52,0.25,-0.45,0.13], [-0.14,-0.41,0.31,-0.41]])
B = np.array([[1,3,1,2], [3,0,2,2]])
import scipy.ndimage
print(scipy.ndimage.sum(A, B, index=[0,1,2,3]))

    You may have to work a little for having the index parameter be exactly what you want. It is the list of the indices you want to get in the result. Maybe the following will be a good starting point:

    print(scipy.ndimage.sum(A,B, index=np.unique(B)))

    but if you know by advance the list of all indices, it will be more efficient to hard-code it here.

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    var tempVerMesh = [];
    var tempVerMesh2 = [];

    var indices = new Uint32Array( tempIndices       );
    var pointsArray = { // for testing
        pointUpper1: new THREE.Vector3(),
        pointUpper2: new THREE.Vector3(),
        pointCenter1: new THREE.Vector3(),
        pointCenter2: new THREE.Vector3(),
        pointLower1: new THREE.Vector3(),
        pointLower2: new THREE.Vector3()
    };

console.log(totalPoints);
    /*function generateUVs(geometry) {
        geometry.computeBoundingBox();

        var max = geometry.boundingBox.max, min = geometry.boundingBox.min;

        var offset = new THREE.Vector3(0 - min.x, 0 - min.y);
        var range = new THREE.Vector3(max.x - min.x, max.y - min.y);
        var faces = geometry.faces;

        geometry.faceVertexUvs[0] = [];

        for (var i = 0; i < faces.length ; i++) {

            var v1 = geometry.vertices[faces[i].a],
                v2 = geometry.vertices[faces[i].b],
                v3 = geometry.vertices[faces[i].c];

            geometry.faceVertexUvs[0].push([
                new THREE.Vector3((v1.x + offset.x)/range.x ,(v1.y + offset.y)/range.y),
                new THREE.Vector3((v2.x + offset.x)/range.x ,(v2.y + offset.y)/range.y),
                new THREE.Vector3((v3.x + offset.x)/range.x ,(v3.y + offset.y)/range.y),
            ]);
        }
        geometry.uvsNeedUpdate = true;
        return geometry;
    }*/
        for (var i = 0; i < totalPoints.lower.length    ; i++) {
            pointsArray.pointCenter1 = totalPoints.center[i];
            //pointsArray.pointCenter2 = totalPoints.center[i + 1];
            pointsArray.pointLower1 = totalPoints.lower[i];
            //pointsArray.pointLower2 = totalPoints.lower[i + 1];
            pointsArray.pointUpper1 = totalPoints.upper[i];
            //pointsArray.pointUpper2 = totalPoints.upper[i + 1];
            tempVerMesh.push(pointsArray.pointCenter1.x, pointsArray.pointCenter1.y, pointsArray.pointCenter1.z);
            tempVerMesh.push(pointsArray.pointLower1.x, pointsArray.pointLower1.y, pointsArray.pointLower1.z);
            tempVerMesh.push(pointsArray.pointLower1.x, pointsArray.pointLower1.y + wallHeight, pointsArray.pointLower1.z);
            tempVerMesh.push(pointsArray.pointCenter1.x, pointsArray.pointCenter1.y + wallHeight, pointsArray.pointCenter1.z);



            tempVerMesh2.push(pointsArray.pointCenter1.x, pointsArray.pointCenter1.y, pointsArray.pointCenter1.z);
            tempVerMesh2.push(pointsArray.pointUpper1.x, pointsArray.pointUpper1.y, pointsArray.pointUpper1.z);

            tempVerMesh2.push(pointsArray.pointUpper1.x, pointsArray.pointUpper1.y + wallHeight, pointsArray.pointUpper1.z );
            tempVerMesh2.push(pointsArray.pointCenter1.x, pointsArray.pointCenter1.y + wallHeight, pointsArray.pointCenter1.z);

        }


    var vertices = new Float32Array(tempVerMesh);
    var vertices2 = new Float32Array(tempVerMesh2);

    //var uvs = new Float32Array(pointUVs);

            geometry.addAttribute('position', new THREE.BufferAttribute(vertices, 3));
            geometry.setIndex(new THREE.BufferAttribute(indices, 1));
            //geometry.addAttribute('uv', new THREE.BufferAttribute(uvs, 2));

            geometry.computeFaceNormals();
            geometry.computeVertexNormals();
    console.log(geometry);

            var mesh = new THREE.Mesh(geometry, material);



    var indices2 = new Uint32Array(tempIndices2);
    geometry2.addAttribute('position', new THREE.BufferAttribute(vertices2, 3));
    geometry2.setIndex(new THREE.BufferAttribute(indices2, 1));



    geometry2.computeFaceNormals();
    geometry2.computeVertexNormals();

   /*var geom = new THREE.Geometry().fromBufferGeometry(geometry2);
    var temp = generateUVs(geom);
    geometry2 = new THREE.BufferGeometry().fromGeometry(temp);*/
    var mesh2 = new THREE.Mesh(geometry2, material2);


    //geometry2.addAttribute('uv', new THREE.BufferAttribute(uvs2, 2));


    return [mesh,mesh2];

};

  camera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 1, 10000);
camera.position.z = 400;

scene = new THREE.Scene();

var arrow;
var rayCaster = new THREE.Raycaster();
var mouse = new THREE.Vector2();

renderer = new THREE.WebGLRenderer();
renderer.setSize( window.innerWidth, window.innerHeight );
document.body.appendChild( renderer.domElement );

renderer.domElement.addEventListener("mousemove", onMouseMove);

var points = {
    pointUpper1: new THREE.Vector3(-70, 0, -20),
    pointUpper2: new THREE.Vector3(130, 0, -20),
    pointCenter1: new THREE.Vector3(-100, 0, 0),
    pointCenter2: new THREE.Vector3(150, 0, 0),
    pointLower1: new THREE.Vector3(-70, 0, 20),
    pointLower2: new THREE.Vector3(130, 0, 20)
};

var totalPoints = {
    center : [new THREE.Vector3(-70, 0, 0),new THREE.Vector3(0, 0, 0),new THREE.Vector3(50, 0, 0),new THREE.Vector3(100, 0, 0),new THREE.Vector3(130, 0, 0)],
    lower : [new THREE.Vector3(-70, 0, 20),new THREE.Vector3(0, 0, 20),new THREE.Vector3(50, 0, 20),new THREE.Vector3(100, 0, 20),new THREE.Vector3(130, 0, 20)],
    upper : [new THREE.Vector3(-70, 0, -20),new THREE.Vector3(0, 0, -20),new THREE.Vector3(50, 0, -20),new THREE.Vector3(100, 0, -20),new THREE.Vector3(130, 0, -20)]
};

var sphere = new THREE.SphereGeometry(2, 10, 10);

function initPoints(){
    var point1mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0xff00}));
    point1mesh.position.copy(points.pointUpper1);
    scene.add(point1mesh);

    var point2mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0x0000ff}));
    point2mesh.position.copy(points.pointUpper2);
    scene.add(point2mesh);

    var point3mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0xff00}));
    point3mesh.position.copy(points.pointCenter1);
    scene.add(point3mesh);

    var point4mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0x0000ff}));
    point4mesh.position.copy(points.pointCenter2);
    scene.add(point4mesh);

    var point5mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0xff00}));
    point5mesh.position.copy(points.pointLower1);
    scene.add(point5mesh);

    var point6mesh = new THREE.Mesh(sphere, new THREE.MeshBasicMaterial({color: 0x0000ff}));
    point6mesh.position.copy(points.pointLower2);
    scene.add(point6mesh);
}
 initPoints();

    var mesh = new wallsGeometry(totalPoints);



function createArrow() {
    var length = 30;
    arrow = new THREE.ArrowHelper(
        THREE.Object3D.DefaultUp,
        new THREE.Vector3(),
        length,
        0xffff00,
        1.5 * length,
        1.25 * length
    );
    arrow.position.z = 10;
    scene.add(arrow);
}
// arrow
createArrow();

function updateArrow(object, point, face) {
    arrow.position.copy(point);
    var normalMatrix = new THREE.Matrix3().getNormalMatrix( object.matrixWorld );
    var normal = face.normal.clone().applyMatrix3( normalMatrix ).normalize();
    arrow.setDirection(normal);
}

function onMouseMove(event) {
    mouse.x = (event.clientX / window.innerWidth) * 2 - 1;
    mouse.y = -(event.clientY / window.innerHeight) * 2 + 1;
    rayCaster.setFromCamera(mouse, camera);

    var intersects = rayCaster.intersectObject(mesh[0], true);
    var i, il, intersect;
    if (intersects[0]) {
        var face = intersects[0].face;
        var point = intersects[0].point;
        var object = intersects[0].object;
        updateArrow(object, point, face);
    }
}
/*         var textureLoader = new THREE.TextureLoader();
    textureLoader.load('./textures/Capture.PNG', function (texture) {
        console.log('texture loaded');
        texture.minFilter = THREE.LinearFilter;

        //mesh[0].material.map = texture;
        var vertexNormalsHelper = new THREE.VertexNormalsHelper( mesh[0], 10 );
        mesh[0].add( vertexNormalsHelper );
    }); */
        scene.add(mesh[0]);

 /*     textureLoader.load('./textures/abc.jpg', function (texture) {
    console.log('texture loaded');
    texture.minFilter = THREE.LinearFilter;
    //mesh[1].material.map = texture;
    var vertexNormalsHelper = new THREE.VertexNormalsHelper( mesh[1], 10 );
    mesh[1].add( vertexNormalsHelper );
}); */
        scene.add(mesh[1]);

//
var Orbitcontrols = new THREE.OrbitControls(camera,renderer.domElement);
Orbitcontrols.update();

}

// render
function render() {
    renderer.render(scene, camera);
}

// animate
function animate() {
    requestAnimationFrame(animate);
    render();
}

    https://jsfiddle.net/simar_aneja/fsmw8znq/6/

    In the fiddle you can see that wall is building properly and you can increase the vertices and loop of creating those indices, in the start. Now I want to add UVs to this bufferGeometry, I tried converting to geometry and then calculated faceVertexUVs, but this is not the right way. Can anyone suggest me the further path where I can attach different textures only at the front side, different on top side. And it should be in such a way that no matter how many vertices comes, Uvs should get calculated based on length of vertices. I have some Idea but not getting how to make it different for diff sides of wall.

    Thanks

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